desiguy wrote:In a formulae a=b(square)c, if b is multiplied by 2 and c is multiplied by 3, what whoudl a be multiplied by ?

4
6
9
12
18

Ans : 12

I know it’s a very very dummbo questin. But my answer is 6. Not sure how its 12 ?

the easiest way to answer this question is to plug in your own numbers and watch what happens. the setup of the answer choices (i.e., all different positive factors) guarantees that any choice of numbers will uniquely yield the correct answer, unless you're unfortunate enough to have selected 0 as one of the initial numbers.

the easiest choice is: b(initial) = c(initial) = 1. then a(initial) = (1^2)(1) = 1.
then you double b and triple c, which means that b(new) = 2 and c(new) = 3. therefore, a(new) = (2^2)(3) = 12.
a has gone from 1 to 12, so it's been multiplied by a factor of 12.
you should find that the same happens regardless of your initial choice of numbers. if it doesn't, then you have miscalculated something.

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if you want to prove this formally, do this:
at the start, the formula is (b^2)(c).
after doubling b and tripling c, you have ((2b)^2)(3c) = (4b^2)(3c) = 12(b^2)(c).
the original quantity has been multiplied by 12.

easier to pick numbers, though - no need to deal with messy things like distributing of exponents